at $412 i would extremely recommend the fx6300+r9-270 with the ram and motherboard i had at $416. if gaming is your primary concern then that is what is going to give you by far the best performance all the way around. the i5-4570 is definitely decent but the fx6300 is not that far behind and in regular desktop apps, itunes, IE, firefox, any MS office apps, etc. even in light video/audio transcoding, your talking a difference between 20 minutes, and 23 minutes, nothing that makes your day a breeze. your never going to be able to tell the difference. what you will be able to tell the difference in is the performance increase of the r9-270 over the gtx750 as the difference is huge. the r9-270 will offer very good 1080p gaming in any game available today and likely most games released in the next year. the gtx750 is going to struggle at 1080p in about 20 of the heaviest games known today like crysis 3, ac4, bf4, tomb raider, metro ll.... etc. if your trying to max out hitman absolution at 1080p, the fx6300+r9-270 is going to do it. intel has some great products and in the much larger budget bracket there is no reason not to go with intel.... but people go with the 4670k+hyper 212 evo=$260, or higher tier cpu since they can be overclocked plus a higher tier gpu so were talking over $600 with mobo and ram. in your budget range with the parts you already have, there is no question the fx6300 is for you and paired with the r9-270 they will offer you very good performance in all games for a few years to come while the gtx750 is more of mediocre/casual gamer gpu.
but since you asked for it, and im not going to recommend it on your budget..... here is a $412 budget with the 4570.....
PCPartPicker part list /
Price breakdown by merchant /
Benchmarks
CPU: Intel Core i5-4570 3.2GHz Quad-Core Processor ($189.96 @ SuperBiiz)
Motherboard: ASRock B85 Pro4 ATX LGA1150 Motherboard ($74.99 @ Newegg)
Memory: A-Data XPG V2 8GB (2 x 4GB) DDR3-1600 Memory ($66.99 @ Newegg)
Video Card: EVGA GeForce GTX 750 1GB Video Card ($99.99 @ Newegg)
Total: $431.93
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-05-23 04:05 EDT-0400)
even at $16 more, its not going to come close to an fx6200+r9-270, and your eventually going to want to upgrade.
get the fx6300, its a great budget processor that offers loads of performance for much less than what intel offers price wise while allowing your stretched budget a very capable r9-270.....
look at its battlefield 3 fps....
http://www.techpowerup.com/reviews/ASUS/R9_270_Direct_Cu_II_OC/7.html
vs the gtx750.... they dont actually have a gtx750 review, but the gtx750ti is about 15-20% more powerful than the gtx750...
http://www.techpowerup.com/reviews/ASUS/GTX_750_Ti_OC/9.html
again...
PCPartPicker part list /
Price breakdown by merchant /
Benchmarks
CPU: AMD FX-6300 3.5GHz 6-Core Processor ($109.98 @ OutletPC)
Motherboard: ASRock 970 Pro3 R2.0 ATX AM3+ Motherboard ($59.99 @ Newegg)
Memory: A-Data XPG V2 8GB (2 x 4GB) DDR3-1600 Memory ($66.99 @ Newegg)
Video Card: Gigabyte Radeon R9 270 2GB WINDFORCE Video Card ($179.99 @ SuperBiiz)
Total: $416.95
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-05-23 04:21 EDT-0400)
down the road you can add a cooler master hyper 212 evo for $30 and easily overclock to 4.5ghz +/- .1ghz for a noticeable overall performance increase.